Related papers: Langevin equation with scale-dependent noise
We consider the nonlinear Schr{\"o}dinger-Langevin equation for both signs of the logarithmic nonlinearity. We explicitly compute the dynamics of Gaussian solutions for large times, which is obtained through the study of a particular…
We consider the linear inverse problem of estimating an unknown signal $f$ from noisy measurements on $Kf$ where the linear operator $K$ admits a wavelet-vaguelette decomposition (WVD). We formulate the problem in the Gaussian sequence…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
In this paper, we study systems of $N$ interacting particles described by the classical and relativistic Langevin dynamics with singular forces and multiplicative noises. For the classical model, we prove the ergodicity, obtaining an…
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer…
A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing…
For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…
The Langevin equation with multiplicative noise and state-dependent transport coefficient has to be always complemented with the proper interpretation rule of the noise, such as the Ito and Stratonovich conventions. Although the…
Kinetic roughening of a randomly growing surface can be modelled by the Kardar-Parisi-Zhang equation with a time-independent (``spatially quenched'' or ``columnar'') random noise. In this paper, we use the field-theoretic renormalization…
We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…
Consider a Langevin process, that is an integrated Brownian motion, constrained to stay on the nonnegative half-line by a partially elastic boundary at 0. If the elasticity coefficient of the boundary is greater than or equal to a critical…
We propose a novel approach based on a Langevin equation for fluctuating motion of the center of mass of granular media fluidized by energy injection from a bottom plate. In this framework, the analytical solution of the Langevin equation…
In this paper, we examine the problem of sampling from log-concave distributions with (possibly) superlinear gradient growth under kinetic (underdamped) Langevin algorithms. Using a carefully tailored taming scheme, we propose two novel…
Let K be a random variable following a truncated exponential distribution. Such distributions are described by a single parameter here denoted by $\gamma$. The determination of $\gamma$ by Maximum Likelihood methods leads to a…
The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for non-separable potentials. Theoretical results are lacking, and numerical calculation of the…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…